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Use the idea from Exercise 53 to find the derivative of

Chapter 4, Problem 54E

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QUESTION:

Problem 54E

Use the idea from Exercise 53 to find the derivative of the of the following function:

        h(x) = xx

REFERENCE EXERCISE:

Let .

a. Using the fact thatuse the chain rule, the product rule, and the formula for the derivative of ln x to show that  

b. Use the result from part a and the fact that

to show that

The idea of taking the logarithm of a function before differentiating is known as logarithmic differentiation.

Questions & Answers

QUESTION:

Problem 54E

Use the idea from Exercise 53 to find the derivative of the of the following function:

        h(x) = xx

REFERENCE EXERCISE:

Let .

a. Using the fact thatuse the chain rule, the product rule, and the formula for the derivative of ln x to show that  

b. Use the result from part a and the fact that

to show that

The idea of taking the logarithm of a function before differentiating is known as logarithmic differentiation.

ANSWER:

Solution:

Step 1 of 2:

In this problem, we need to find the derivative of the function

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